Question

Convert
(a) 365 days into weeks and days
(b) 86 months into years
(c) 784 days into months and days

Answer 1

Hint:We first find the relation between different units of time. The measurements are common in measurement units. We find the relation as 1 year being equal to 12 months, 30 days being equal to 1 month, 7 days being into 1 week. We use the unitary system, to find the solution of the given conversion.

Complete step by step answer:
We need to convert the time by changing its unit from months to years. We find the relation between months and years as 1 year being equal to 12 months, 30 days being equal to 1 month, 7 days being 1 week. We already have that in the unitary system. The unitary method is a method in which we find the value of a unit and then the value of a required number of units. The unitary method is also used to find the value of a single unit from a given multiple.

(a) We need the equivalent time of 365 days into weeks and days. We divide 365 by 7 and get
$7\stackrel{52}{\overline{)\begin{array}{rl}& 365\\ & \underset{―}{35}\\ & 15\\ & \underset{―}{14}\\ & 1\end{array}}}$
We get 52 total weeks and then we have 1 leftover day.
Therefore, 365 days is equal to 52 weeks and 1 day.

We need the equivalent time of 86 months in years. We divide 86 by 12 and get
$12\stackrel{7}{\stackrel{―}{)\begin{array}{rl}& 86\\ & \underset{―}{84}\\ & 2\end{array}}}$
We get 7 total years and then we have 2 leftover months. These can be denoted in years as ${\displaystyle \frac{2}{12}}={\displaystyle \frac{1}{6}}$ years. Therefore, 86 months is equal to ${\displaystyle \frac{86}{12}}=7+{\displaystyle \frac{1}{6}}=7{\displaystyle \frac{1}{6}}$ years.

(c) We need the equivalent time of 784 days into months and days. We divide 784 by 30 and get,
$30\stackrel{26}{\overline{)\begin{array}{rl}& 784\\ & \underset{―}{60}\\ & 184\\ & \underset{―}{180}\\ & 4\end{array}}}$
We get 26 total months and then we have 4 leftover days. Therefore, 784 days is equal to 26 months and 4 days.

Note: The months and years are units of measurement for time in both the US customary units and the metric systems of measurement. If the required unit is one then we have to keep using fraction or decimal form. It is not mentioned in particular that only we can use mixed forms of units. That’s why we kept 784 days as a mixed form of months and days. We converted 86 to $7{\displaystyle \frac{1}{6}}$ fraction form to convert in one single unit.